The Dutch recieved 16000 suits of clothing from the British. The coatees, caps and sleeved waistcoats were not in accordance with the Dutch patterns and so most of these were distributed to the provinces to aid them in clothing the militia. A number was also send to the provinces to serve as pattern for the remainder of the clothing.
Remarks on details of dress are spread out over many letters and reports. The first one I found now is this one:

Nationaal Archief, Den Haag, Ministerie van Oorlog: Verbaalarchief (gewoon en geheim), number entry 2.13.01, inventory number 64, Letter of 5 August 1814 nr. 5-6, attachment: a report on the quality of the clothing issued to the bataillon by the province of Gelderland.
"Vesten met mouwen. bestaan uit tweederlei stoffe, zoodat het lijf uit carsaij en de mouwen uit een soort van zoogenaamde baai is zamengesteld [...]"
[Defending remark:] "de mouwen zijn van flanel even als het model, met dat onderscheid echter, dat het model engelsch is [...]
Translation:Sleeved waistcoats. are made of two kinds of material, so that the body is made of kersey and the sleeves from a kind of baize [...]
[Defending remark:] the sleeves are made of flannel, like the pattern, which pattern is English

I'm going to have to bow to the mounting evidence here and say that the British army fatigue jacket of the early 19th century had a cheap, white kersey body, (meaning a twill weave of cotton warp and woolen weft), and white, all woolen serge flannel sleeves.
Both are twill weaves and would look similar to each other.
From the evidence it would appear that the rank and file jackets were unlined, had four piece bodies and two piece sleeves. It would also appear the NCO jackets may have been lined and made entirely of the more pricey serge flannel.
Many of the jackets had tall collars (but not as tall as the regimentals), cuffs and straps of facing colour. Many seem to have been pointed at the waist backs.